Future reliability prediction based on system operational and performance data modelling

ABSTRACT

Systems, methods, and apparatuses for improving future reliability prediction of a measurable system by receiving operational and performance data, such as maintenance expense data, first principle data, and asset reliability data via an input interface associated with the measurable system. A plurality of category values may be generated that categorizes the maintenance expense data by a designated interval using a maintenance standard that is generated from one or more comparative analysis models associated with the measurable system. The estimated future reliability of the measurable system is determined based on the asset reliability data and the plurality of category values and the results of the future reliability are displayed on an output interface.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of, and claims thebenefit of, U.S. Application Serial No. 16/566,845, filed Sep. 10, 2019,which is a continuation application of, and claims the benefit of U.S.Application Serial No. 14/684,358, filed Apr. 11, 2015, now issued asU.S. Pat. No. 10,409,891, which claims the benefit, and prioritybenefit, of U.S. Provisional Pat. Application Serial No. 61/978,683filed Apr. 11, 2014, titled “System and Method for the Estimation ofFuture Reliability Based on Historical Maintenance Spending,” thedisclosure of which is incorporated herein in their entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable.

REFERENCE TO A MICROFICHE APPENDIX

Not applicable.

FIELD OF TECHNOLOGY

The disclosure generally relates to the field of modelling andpredicting future reliability of measurable systems based on operationaland performance data, such as current and historical data regardingproduction and/or cost associated with maintaining equipment. Moreparticularly, but not by way of limitation, embodiments within thedisclosure perform comparative performance analysis and/or determinemodel coefficients used to model and estimate future reliability of oneor more measurable systems.

BACKGROUND

Typically, for repairable systems, there is a general correlationbetween the methodology and process used to maintain the repairablesystems and future reliability of the systems. For example, individualswho have owned or operated a bicycle, a motor vehicle, and/or any othertransportation vehicle are typically aware that the operating conditionand reliability of the transportation vehicles can be dependent to someextent on the degree and quality of activities to maintain thetransportation vehicles. However, although a correlation may existbetween maintenance quality and future reliability, quantifying and/ormodelling this relationship may be difficult. In addition to repairablesystems, similar relationships and/or correlations may be true for awide-variety of measureable systems where operation and/or performancedata is available or otherwise where data used to evaluate a system maybe measured.

Unfortunately, the value or amount of maintenance spending may notnecessarily be an accurate indicator for predicting future reliabilityof the repairable system. Individuals can accrue maintenance costs thatare spent on task items that have relatively minimum effect on improvingfuture reliability. For example, excessive maintenance spending mayoriginate from actual system failures rather than performing preventivemaintenance related tasks. Generally, system failures, breakdowns,and/or unplanned maintenance can cost more than a preventive and/orpredictive maintenance program that utilizes comprehensive maintenanceschedules. As such, improvements need to be made that improve theaccuracy for modelling and predicting future reliability of ameasureable system.

BRIEF SUMMARY

The following presents a simplified summary of the disclosed subjectmatter in order to provide a basic understanding of some aspects of thesubject matter disclosed herein. This summary is not an exhaustiveoverview of the technology disclosed herein. It is not intended toidentify key or critical elements of the invention or to delineate thescope of the invention. Its sole purpose is to present some concepts ina simplified form as a prelude to the more detailed description that isdiscussed later.

In one embodiment, a system for modelling future reliability of afacility based on operational and performance data, comprising an inputinterface configured to: receive maintenance expense data correspondingto a facility; receive first principle data corresponding to thefacility; and receive asset reliability data corresponding to thefacility. The system may also comprise a processor coupled to anon-transitory computer readable medium, wherein the non-transitorycomputer readable medium comprises instructions when executed by theprocessor causes the apparatus to: obtain one or more comparativeanalysis models associated with the facility; obtain a maintenancestandard that generates a plurality of category values that categorizesthe maintenance expense data by a designated interval based upon atleast the maintenance expense data, the first principle data, and theone or more comparative analysis models; and determine an estimatedfuture reliability of the facility based on the asset reliability dataand the plurality of category values. The computer node may alsocomprise a user interface that displays the results of the futurereliability.

In another embodiment, a method for modelling future reliability of ameasurable system based on operational and performance data, comprising:receiving maintenance expense data via an input interface associatedwith a measurable system; receiving first principle data via an inputinterface associated with the measureable system; receiving assetreliability data via an input interface associated with the measureablesystem; generating, using a processor, a plurality of category valuesthat categorizes the maintenance expense data by a designated intervalusing a maintenance standard that is generated from one or morecomparative analysis models associated with the measureable system;determining, using a processor, an estimated future reliability of themeasureable system based on the asset reliability data and the pluralityof category values; and outputting the results of the estimated futurereliability using an output interface.

In yet another embodiment, an apparatus for modelling future reliabilityof an equipment asset based on operational and performance data,comprising an input interface comprising a receiving device configuredto: receive maintenance expense data corresponding to an equipmentasset; receive first principle data corresponding to the equipmentasset; receive asset reliability data corresponding to the equipmentasset; a processor coupled to a non-transitory computer readable medium,wherein the non-transitory computer readable medium comprisesinstructions when executed by the processor causes the apparatus to:generate a plurality of category values that categorizes the maintenanceexpense data by a designated interval from a maintenance standard; anddetermine an estimated future reliability of the facility comprisingestimated future reliability data based on the asset reliability dataand the plurality of category values; and an output interface comprisinga transmission device configured to transmit a processed data set thatcomprises the estimated future reliability data to a control center forcomparing different equipment assets based on the processed data set.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a flow chart of an embodiment of a data analysis method thatreceives data from one or more various data sources relating to ameasureable system, such as a power generation plant;

FIG. 2 is a schematic diagram of an embodiment of a data compilationtable generated in the data compilation of the data analysis methoddescribed in FIG. 1 ;

FIG. 3 is a schematic diagram of an embodiment of a categorizedmaintenance table generated in the categorized time based maintenancedata of the data analysis method described in FIG. 1 ;

FIG. 4 is a schematic diagram of an embodiment of a categorizedreliability table generated in the categorized time based reliabilitydata of the data analysis method described in FIG. 1 ;

FIG. 5 is a schematic diagram of an embodiment of a future reliabilitydata table generated in the future reliability prediction of the dataanalysis method described in FIG. 1 ;

FIG. 6 is a schematic diagram of an embodiment of a future reliabilitystatistic table generated in the future reliability prediction of thedata analysis method described in FIG. 1 ;

FIG. 7 is a schematic diagram of an embodiment of a user interface inputscreen configured to display information a user may need to input todetermine a future reliability prediction using the data analysis methoddescribed in FIG. 1 ;

FIG. 8 is a schematic diagram of an embodiment of a user interface inputscreen configured for EFOR prediction using the data analysis methoddescribed in FIG. 1 ;

FIG. 9 is a schematic diagram of an embodiment of a computing node forimplementing one or more embodiments.

FIG. 10 is a flow chart of an embodiment of a method for determiningmodel coefficients for use in comparative performance analysis of ameasureable system, such as a power generation plant.

FIG. 11 is a flow chart of an embodiment of a method for determiningprimary first principle characteristics as described in FIG. 10 .

FIG. 12 is a flow chart of an embodiment of a method for developingconstraints for use in solving the comparative analysis model asdescribed in FIG. 10 .

FIG. 13 is a schematic diagram of an embodiment of a model coefficientmatrix for determining model coefficients as described in FIGS. 10-12 .

FIG. 14 is a schematic diagram of an embodiment of a model coefficientmatrix with respect to a fluidized catalytic cracking unit (Cat Cracker)for determining model coefficients for use in comparative performanceanalysis as illustrated in FIGS. 10-12 .

FIG. 15 is a schematic diagram of an embodiment of a model coefficientmatrix with respect to the pipeline and tank farm for determining modelcoefficients for use in comparative performance analysis as illustratedin FIGS. 10-12 .

FIG. 16 is a schematic diagram of another embodiment of a computing nodefor implementing one or more embodiments.

While certain embodiments will be described in connection with thepreferred illustrative embodiments shown herein, it will be understoodthat it is not intended to limit the invention to those embodiments. Onthe contrary, it is intended to cover all alternatives, modifications,and equivalents, as may be included within the spirit and scope of theinvention as defined by claims that are included within this disclosure.In the drawing figures, which are not to scale, the same referencenumerals are used throughout the description and in the drawing figuresfor components and elements having the same structure, and primedreference numerals are used for components and elements having a similarfunction and construction to those components and elements having thesame unprimed reference numerals.

DETAILED DESCRIPTION

It should be understood that, although an illustrative implementation ofone or more embodiments are provided below, the various specificembodiments may be implemented using any number of techniques known bypersons of ordinary skill in the art. The disclosure should in no way belimited to the illustrative embodiments, drawings, and/or techniquesillustrated below, including the exemplary designs and implementationsillustrated and described herein. Furthermore, the disclosure may bemodified within the scope of the appended claims along with their fullscope of equivalents.

Disclosed herein are one or more embodiments for estimating futurereliability of measurable systems. In particular, one or moreembodiments may obtain model coefficients for use in comparativeperformance analysis by determining one or more target variables and oneor more characteristics for each of the target variables. The targetvariables may represent different parameters for a measureable system.The characteristics of a target variable may be collected and sortedaccording to a data collection classification. The data collectionclassification may be used to quantitatively measure the differences incharacteristics. After collecting and validating the data, a comparativeanalysis model may be developed to compare predicted target variables toactual target variables for one or more measureable systems. Thecomparative analysis model may be used to obtain a set of complexityfactors that attempts to minimize the differences in predicted versusactual target variable values within the model. The comparative analysismodel may then be used to develop a representative value for activitiesperformed periodically on the measurable system to predict futurereliability.

FIG. 1 is a flow chart of an embodiment of a data analysis method 60that receives data from one or more various data sources relating to ameasureable system, such as a power generation plant. The data analysismethod 60 may be implemented by a user, a computing node, orcombinations thereof to estimate future reliability of a measureablesystem. In one embodiment, the data analysis method 60 may automaticallyreceive updated available data, such as updated operational andperformance data, from various data sources, update one or morecomparative analysis models using the received updated data, andsubsequently provide updates on estimations of future reliability forone or more measurable system. A measurable system is any system that isassociated with performance data, conditioned data, operation data,and/or other types of measurable data (e.g., quantitative and/orqualitative data) used to evaluate the status of the system. Forexample, the measurable system may be monitored using a varietyparameters and/or performance factors associated with one or morecomponents of the measurable system, such as in a power plant, facility,or commercial building. In another embodiment, the measurable system maybe associated with available performance data, such as stock prices,safety records, and/or company finance. The terms “measurable system,”“facility,” “asset,” or “plant,” may be used interchangeably throughoutthis disclosure.

As shown in FIG. 1 , the data from the various data sources may beapplied at different computational stages to model and/or improve futurereliability predictions based on available data for a measureablesystem. In one embodiment, the available data may be current andhistoric maintenance data that relates to one or more measurableparameters of the measureable system. For instance, in terms ofmaintenance and repairable equipment, one way to describe maintenancequality is to compute the annual or periodic maintenance cost for ameasurable system, such as an equipment asset. The annual or periodicmaintenance number denotes the amount of money spent over a given periodof time, which may not necessarily accurately reflect futurereliability. For example, a vehicle owner may spend money to wash andclean a vehicle weekly, but spend relatively little or no money formaintenance that could potentially increase the future reliability ofcar, such as replacing tires and/or oil or filter changes. Although theannual maintenance costs for washing and cleaning the car may be asizeable number when performed frequently, the maintenance task and/oractivities of washing and cleaning may have relatively little or noeffect on improving a car’s reliability.

FIG. 1 illustrates that the data analysis method 60 may be used topredict the future Equivalent Forced Outage Rate (EFOR) estimates forRankine and Brayton cycle based power generation plants. EFOR is definedas the hours of unit failure (e.g., unplanned outage hours andequivalent unplanned derated hours) given as a percentage of the totalhours of the availability of that unit (e.g., unplanned outage,unplanned derated, and service hours). As shown in FIG. 1 , within afirst data collection stage, the data analysis method 60 may initiallyobtain asset maintenance expense data 62 and asset unit first principledata or other asset-level data 64 that relate to the measureable datasystem, such as a power generation plant. Asset maintenance expense data62 for a variety of facilities may typically be obtained directly fromthe plant facilities. The asset maintenance expense data 62 mayrepresent the cost associated with maintaining a measurable system for aspecified time period (e.g. in seconds, minutes, hours, months, andyears). For example, the asset maintenance expense data 62 may be theannual or periodic maintenance cost for one or more measurable systems.The asset unit first principle data or other asset-level data 64 mayrepresent physical or fundamental characteristics of a measurablesystem. For example, the asset unit first principle data or otherasset-level data 64 may be operational and performance data, such asturbine inlet temperature, age of the asset, size, horsepower, amount offuel consumed, and actual power output compared to nameplate thatcorrespond to one more measureable systems.

The data obtained in the first data collection stage may be subsequentlyreceived or entered to generate a maintenance standard 66. In oneembodiment, the maintenance standard 66 may be an annualized maintenancestandard where a user supplies in advance one or more modellingequations that compute the annualized maintenance standard. The resultmay be used to normalize the asset maintenance expense data 62 andprovide a benchmark indicator to measure the adequacy of spendingrelative to other power generation plants of a similar type. In oneembodiment, a divisor or standard can be computed based on the assetunit’s first principle data or other asset-level data 104, which areexplained in more detail in FIGS. 10-12 . Alternative embodiments mayproduce the maintenance standard 66, for example, from simple regressionanalysis with data from available plant related target variables.

Maintenance expenses for the replacement of components that normallywear out over time may occur at different time intervals causingvariations in periodic maintenance expenses. To address the potentialissue, the data analysis method 60 may generate a maintenance standard66 that develops a representative value for maintenance activities on aperiodic basis. For example, to generate the maintenance standard 66,the data analysis method 60 may normalize maintenance expenses to someother time period. In another embodiment, the data analysis method 60may generate a periodic maintenance spending divisor to normalize theactual periodic maintenance spending to measure the under (ActualExpense/Divisor ratio <1) or over (Actual Expense/Divisor ratio >1)spending. The maintenance spending divisor may be a value computed froma semi-empirical analysis of data using asset maintenance expense data62, asset unit first principle data or other asset-level data 64 (e.g.,asset characteristics), and/or documented expert opinions. In thisembodiment, an asset unit first principle data or other asset-level data64, such as plant size, plant type, and/or plant output, in conjunctionwith computed annualized maintenance expenses may be used to compute astandard maintenance expense (divisor) value for each asset in theanalysis as described in U.S. Pat. 7,233,910, filed Jul. 18, 2006,titled “System and Method for Determining Equivalency Factors for use inComparative Performance Analysis of Industrial Facilities,” which ishereby incorporated by reference as if reproduced in their entirety. Thecalculation may be performed with a historical dataset that may includethe assets under current analysis. The maintenance standard calculationmay be applied as a model that includes one or more equations formodelling a measurable system’s future reliability prediction. The dataused to compute the maintenance standard divisor may be supplied by theuser, transferred from a remote storage device, and/or received via anetwork from a remote network node, such as a server or database.

FIG. 1 illustrates that the data analysis method 60 may receive theasset reliability data 400 in a second data collection stage. The assetreliability data 70 may correspond to each of the measureable systems.The asset reliability data 70 is any data that corresponds todetermining the reliability, failure rate and/or unexpected down time ofa measurable system. Once the data analysis method 60 receives the assetreliability data 70 for each measureable system, the data analysismethod 60 may be compiled and linked to the measureable systems’maintenance spending ratio, which may be associated or shown on the sameline as the other measureable systems and time specific data. For powergeneration plants, the asset reliability data 70 may be obtained fromthe National American Electric Reliability Corporation’s GeneratingAvailability Database (NERC-GADS). Other types of measureable systemsmay also obtain asset reliability data 70 from similar databases.

At data compilation 68, the data analysis method 60 compiles thecomputed maintenance standard 66, asset maintenance expense data 62, andasset reliability data 70 into a common file. In one embodiment, thedata analysis method 60 may add an additional column to the dataarrangement within the common file. The additional column may representthe ratios of actual annualized maintenance expenses and the computedstandard value for each measureable system. The data analysis method 60may also add another column within the data compilation 68 thatcategorizes the maintenance spending ratios divided by some percentileintervals or categories. For example, the data analysis method 60 mayuse nine different intervals or categories to categorize the maintenancespending ratios.

In the categorized time based maintenance data 72, the data analysismethod 60 may place the maintenance category values into a matrix, suchas a 2x2 matrix, that defines each measureable system, such as a powergeneration plant and time unit. In the categorized time basedreliability data 74, the data analysis method 60 assigns the reliabilityfor each measureable system using the same matrix structure as describedin the categorized time based maintenance data 72. In the futurereliability prediction 76, the data is statistically analyzed from thecategorized time based maintenance data 72 and the categorized timebased reliability data 74 to compute an average and/or other statisticalcalculations to determine the future reliability of the measureablesystem. The number of computed time periods or years in the future maybe a function of the available data, such as the asset maintenanceexpense data 62, asset reliability data 70, and asset unit firstprinciple data or other asset-level data. For instance, the futureinterval may be one year in advance because of the available data, butother embodiments may utilize selection of two or three years in thefuture depending on the available data sets. Also, other embodiments mayuse other time periods besides years, such as seconds, minutes, hours,days, and/or months, depending on the granularity of the available data.

It should be noted that while the discussion involving FIG. 1 wasspecific to power generation plants and industry, the data analysismethod 60 may be also applied to other industries where similarmaintenance and reliability databases exist. For example, in therefining and petrochemical industries, maintenance and reliability dataexists for process plants and/or other measureable systems over manyyears. Thus, the data analysis method 60 may also forecast futurereliability for process plants and/or other measureable systems usingcurrent and previous year maintenance spending ratio values. Otherembodiments of the data analysis method 60 may also be applied to thepipeline industry and maintenance of buildings (e.g., office buildings)and other structures.

Persons of ordinary skill in the art are aware that other industriesreliability may utilize a wide variety of metrics or parameters for theasset reliability data 70 that differ from the power industry’s EFORmeasure that was applied in FIG. 1 . For example, other appropriateasset reliability data 70 that could be used in the data analysis method60 include but are not limited to “unavailability,” “availability,”“commercial unavailability,” and “mean time between failures.” Thesemetrics or parameters may have definitions often unique to a givensituation, but their general interpretation is known to one skilled inthe reliability analysis and reliability prediction field.

FIG. 2 is a schematic diagram of an embodiment of a data compilationtable 250 generated in the data compilation 68 of the data analysismethod 60 described in FIG. 1 . The data compilation table 250 may bedisplayed or transmitted using an output interface, such a graphic userinterface or to a printing device. FIG. 2 illustrates that the datacompilation table 250 comprises a client number column 252 thatindicates the asset owner, a plant name column 254 that indicates themeasureable system and/or where the data is being collected, and a studyyear column 256. As shown in FIG. 2 , each asset owner within table 200owns a single measureable system. In other words, each of themeasureable systems is owned by different asset owners. Otherembodiments of the data compilation table 250 may have a plurality ofmeasureable systems owned by the same asset owner. The study year column256 refers to the time period of when the data is collected or analyzedfrom the measureable system.

The data compilation table 250 may comprise additional columnscalculated using the data analysis method 60. The computed maintenance(Mx) standard column 258 may comprise data values that represent thecomputational result of the maintenance standard as described inmaintenance standard 66 in FIG. 1 . Recall that in one embodiment, themaintenance standard 66 may be generated as described in as described inU.S. Pat. 7,233,910. Other embodiments may compute results of themaintenance standard known by persons of ordinary skill in the art. Theactual annualized Mx expense column 260 may comprise computed datavalues that represent the normalized actual maintenance data based onthe maintenance standard as described in maintenance standard 66 in FIG.1 . The actual maintenance data may be the effective annual expense overseveral years (e.g., about 5 years). The ratio actual (Act) Mx/standard(Std) Mx column 262 may comprise data values that represent thenormalized maintenance spending ratio that is used to assess theadequacy or effectiveness of maintenance spending in relationship tofuture reliability. The last column, the EFOR column 266 comprises datavalues that represent the reliability or, in this case, un-reliabilityvalue for the current time period. The data values of the EFOR column266 is a summation of hours of unplanned outages and de-rates divided bythe hours in the operating period. The definition of EFOR in thisexample follows the notation as documented in NERC-GADS literature. Forexample, an EFOR value of 9.7 signifies that the measureable system waseffectively down about 9.7% of its operating period due to unplannedoutage events.

The Act Mx/Std Mx: Decile column 264 may comprises data values thatrepresent the maintenance spending ratios categorized into valueintervals relating to distinct ranges as discussed in data compilation68 in FIG. 1 . Duo-deciles, deciles, sextiles, quintiles, or quartilescould be used, but in this example the data is divided into ninecategories based on the percentile ranking of the maintenance spendingratio data values found in the Act Mx/Std mx column 262. The number ofintervals or categories used to divide the maintenance spending ratiosmay depend on the dataset size, where more detailed divisions that arestatistically possible may be generated with a relatively larger datasetsize. A variety of methods or algorithms known by persons of ordinaryskill in the art may be used to determine the number of intervals basedon the dataset size. The transformation of maintenance spending ratiosinto ordinal categories may serve as a reference to assign future EFORreliability values that were actually achieved.

FIG. 3 is a schematic diagram of an embodiment of a categorizedmaintenance table 350 generated in the categorized time basedmaintenance data 72 of the data analysis method 60 described in FIG. 1 .The categorized maintenance table 350 may be displayed or transmittedusing an output interface, such a graphic user interface or to aprinting device. Specifically, the categorized maintenance table 350 isa transformation of the maintenance spending ratio ordinal category datavalues found within FIG. 2 ’s data compilation table 250. FIG. 3illustrates that the plant name column 352 may identify the differentmeasureable systems. The year columns 354-382 represent the differentyears or time periods for each of the measureable systems. Using FIG. 3as an example, Plants 1 and 2 have data values from 1999-2013 and Plants3 and 4 have data values from 2002-2013. The type of data found withinthe year columns 354-382 are substantially similar to the type of datawithin the Act Mx/Std Mx: Decile column 264 in FIG. 2 . In particular,the type of data within the year columns 354-382 represent intervalsrelating to distinct ranges of the maintenance spending ratio and may begenerally referred to as the maintenance spending ratio ordinalcategory. For example, for the year 1999, Plant 1 has a maintenancespending ratio categorized as “5” and Plant 2 has a maintenance spendingratio categorized as “1.”

FIG. 4 is a schematic diagram of an embodiment of a categorizedreliability table 400 generated in the categorized time basedreliability data 74 of the data analysis method 60 described in FIG. 1 .The categorized reliability table 400 may be displayed or transmittedusing an output interface, such a graphic user interface or to aprinting device. The categorized reliability table 400 is atransformation of EFOR data values found within FIG. 2 ’s datacompilation table 250. FIG. 4 illustrates that the plant name column 452may identify the different measureable systems. The year columns 404-432represent the different years for each of the measureable systems. UsingFIG. 4 as an example, Plants 1 and 2 have data values from 1999-2013 andPlants 3 and 4 have data values from 2002-2013. The type of data foundwithin the year columns 354-382 are substantially similar to the type ofdata within the EFOR column 266 in FIG. 2 . In particular, the type ofdata within the year columns 354-382 represents EFOR values that denotethe percentage of unplanned outage events. For example, for the year1999, Plant 1 has an EFOR 2.4, which indicates that Plant 1 was downabout 2.4% of its operating period due to unplanned outage events andPlant 2 has an EFOR of 5.5, which indicates that Plant 1 was down about5.5% of its operating period due to unplanned outage events.

FIG. 5 is a schematic diagram of an embodiment of a future reliabilitydata table 500 generated in the future reliability prediction 76 of thedata analysis method 60 described in FIG. 1 . The future reliabilitydata table Y may be displayed or transmitted using an output interface,such a graphic user interface or to a printing device. The process ofcomputing future reliability starts with selecting the futurereliability interval, for example, in FIG. 5 , the interval is about twoyears. After selecting the future reliability interval, the data shownin FIG. 3 is scanned horizontally or a row by row basis within thecategorized maintenance table 350 where entries for a selected row inthe categorized maintenance table 350 to determiner rows that areseparated out only by about one year. Using FIG. 3 for example, the rowassociated with Plant 1 would satisfy the data separation of about oneyear, but Plant 11 would not because Plant 11 in the categorizedmaintenance table 350 has a data gap between years 2006 and 2008. Inother words, Plant 11 is missing data at year 2007, and thus, entriesfor the Plant 11 are not separated out about one year. Other embodimentsmay select future reliability interval with different time intervalsmeasured in seconds, minutes, hours, days, and/or months in the future.The time interval used to determine future reliability depends on thelevel of data granularity.

The maintenance spending ratio ordinal category for each separated rowcan be subsequently paired up with a time forward EFOR value from thecategorized reliability data table 400 to form ordered pairs. Thegenerated order pairs comprise the maintenance spending ratio ordinalcategory and the time forward EFOR value. Since the selected futurereliability interval is about two years, the year associated with themaintenance spending ratio ordinal category and the year for the EFORvalue within the generated order pairs may be two years apart. Someexamples of these ordered pairs for the same plant or same row foranalyzing future about two years in advance are:

-   First order pair: (maintenance spending ratio ordinal category in    1999, EFOR value 2001)-   Second order pair: (maintenance spending ratio ordinal category in    2000, EFOR value 2002)-   Third order pair: (maintenance spending ratio ordinal category in    2001, EFOR value 2003)-   Fourth order pair: (maintenance spending ratio ordinal category in    2002, EFOR value 2004)

As shown above, in each of the order pairs, the years that separate themaintenance spending ratio ordinal category and the EFOR value are basedon the future reliability interval, which is about two years. To formthe order pairs, the matrices of FIGS. 3 and 4 may be scanned forpossible data pairs separated by two years (e.g., 1999 and 2001). Inthis case, the middle year data is not used (e.g., 2000) for the datapairs. This process can repeated for other future reliability intervals(e.g., one year in advance of the maintenance ratio ordinal value at thediscretion of the user and the information desired from the analysis).Moreover, the order pair examples above depict that the maintenancespending ratio ordinal category and EFOR values are incremented by onefor each of the order pairs. For example, the first order pair has amaintenance spending ratio ordinal category in 1999 and the second orderpair has a maintenance spending ratio ordinal category in 2000.

The different maintenance spending ratio ordinal category value is usedto place the corresponding time forward EFOR value into the correctcolumn within the future reliability data table 500. As shown in FIG. 5, column 502 comprises EFOR values with a maintenance spending ratioordinal category of “1”; column 504 comprises EFOR values with amaintenance spending ratio ordinal category of “2”; column 506 comprisesEFOR values with a maintenance spending ratio ordinal category of “3”;column 508 comprises EFOR values with a maintenance spending ratioordinal category of “4”; column 510 comprises EFOR values with amaintenance spending ratio ordinal category of “5”; column 512 comprisesEFOR values with a maintenance spending ratio ordinal category of “6”;column 514 comprises EFOR values with a maintenance spending ratioordinal category of “7”; column 516 comprises EFOR values with amaintenance spending ratio ordinal category of “8”; and column 518comprises EFOR values with a maintenance spending ratio ordinal categoryof “9.”

FIG. 6 is a schematic diagram of an embodiment of a future reliabilitystatistic table 600 generated in the future reliability prediction 76 ofthe data analysis method 60 described in FIG. 1 . The future reliabilitystatistic table 600 may be displayed or transmitted using an outputinterface, such a graphic user interface or to a printing device. InFIG. 6 , the future reliability statistic table 600 comprises themaintenance spending ratio ordinal category columns 602-618. As shown inFIG. 6 , each of the maintenance spending ratio ordinal category columns602-618 corresponds to a maintenance spending ratio ordinal category.For example, maintenance spending ratio ordinal category column 602corresponds to the maintenance spending ratio ordinal category “1” andmaintenance spending ratio ordinal category column 604 corresponds tothe maintenance spending ratio ordinal category “2.” The compiled datain each maintenance ratio ordinal value column 602-618 is analyzed usingthe data within the future reliability data table 500 to compute variousstatistics that indicate future reliability information. As shown inFIG. 6 , rows 620, 622, and 624 represent the average, median, and thevalue at the 90^(th) percentile distribution for the future reliabilitydata for each of the maintenance ratio ordinal values. In FIG. 6 , thefuture reliability information is interpreted as the future reliabilitypredictions or EFOR for a measurable system that the current year has aspecific maintenance spending ratio ordinal values.

Future EFOR predictions can be computed utilizing current and previousyears’ maintenance spending ratios. For multi-year cases, themaintenance spending ratios are computed by adding the annualizedexpenses for the years, and dividing by the sum of the maintenancestandards for the previous years. This way the spending ratio reflectsperformance over several years relative to a general standard that isthe summation of the standards computed for each of the included years.

FIG. 7 is a schematic diagram of an embodiment of a user interface inputscreen 700 configured to display information a user may need to input todetermine a future reliability prediction 76 using the data analysismethod 60 described in FIG. 1 . The user interface input screen 700comprises a measurable system selection column 702 that a user may useto select the type of measureable system. Using FIG. 7 as an example,the user may select the “Coal-Rankine” plant as the type of powergeneration unit or measureable system. Other selections shown in FIG. 7include “Gas-Rankine” and “Combustion Turbine.” Once the type ofmeasureable system is selected, the user interface input screen 700 maygenerate the required data items 704 associated with the type ofmeasureable system a user selects. The data items 704 that appear withinthe user interface input screen 700 may vary depending on the selectedmeasureable system within the measurable system selection column 702.FIG. 7 illustrates that a user has selected a Coal-Rankine plant and theuser may enter all fields that are shown blank with an underscore line.This may also include the annualized maintenance expenses for thespecific year. In other embodiments, the blank fields may be enteredusing information received from a remote data storage or via a network.The current model also allows a user, if desired, to enter previous yeardata to add more information for the future reliability prediction.Other embodiments may import and obtain the additional information froma storage medium or via network.

Once this information is entered, the calculation fields 706, such asannual maintenance standard (k$) field and risk modification factorfield, at the bottom of user interface input screen 700 mayautomatically populate based on the information entered by the user. Theannual maintenance standard (k$) field may be computed substantiallysimilar to the computed MX standard 258 shown in FIG. 6 . The riskmodification factor field may represent the overall risk modificationfactor for the comparative analysis model and may be a ratio of thecomputed future one year average EFOR to the overall average EFOR. Inother words, the data result automatically generated within the riskmodification factor field represents the relative reliability risk of aparticular measurable system compared to an overall average.

FIG. 8 is a schematic diagram of an embodiment of a user interface inputscreen 800 configured for EFOR prediction using the data analysis method60 described in FIG. 1 . In FIG. 8 , there are several results forconsideration by the user. The curve 802 is as a ranking curve thatrepresents the distribution of maintenance spending ratios, and thetriangle 804 on the curve 802 shows the location of the currentmeasureable system or measureable system under consideration by a user(e.g., the “Coal-Rankine” plant selected in FIG. 7 ). The user interfaceinput screen 800 illustrates to a user both the range of knownperformance and where in the range the specific measureable system underconsideration falls. The numbers below this curve are the quintilevalues of the maintenance spending ratio, where the maintenance spendingratios are categorized into five different value intervals. The dataresults illustrated in FIG. 8 were computed for quintiles in thisembodiment; however, other divisions are possible based on the amount ofdata available and the objectives of the analyst and user.

The histogram 806 represents the average 1 year future EFOR dependent onthe specific quintile the maintenance spending ratio falls under. Forexample, the lowest 1 year future EFOR appears for plants that have amaintenance spending ratio in the second quintile or have maintenancespending ratios of about 0.8 and about 0.92. This level of spendingsuggests the unit is successfully managing the asset with the betterpractices that assures long term reliability. Notice that the firstquintile or plants with maintenance spending ratios of about zero toabout 0.8 actually exhibits a higher EFOR value suggesting thatoperators are not performing the required or sufficient maintenance toproduce long-term reliability. If a plant falls into the fifth quintile,one interpretation of this is that operators could be overspendingbecause of breakdowns. Since maintenance costs from unplannedmaintenance events can be larger than planned maintenance expenses, ahigh maintenance spending ratios may produce high EFOR values.

The dotted line 810 represents the average EFOR for all of the dataanalyzed for the current measureable system. The diamond 812 representsthe actual 1 year future EFOR estimate located directed above thetriangle 804, which represents the maintenance spending ratio. The twosymbols correlate or connect the current maintenance spending levels,triangle 804, to a future 1 year estimate of EFOR, the diamond 812.

FIG. 10 is a flow chart of an embodiment of a method 100 for determiningmodel coefficients for use in comparative performance analysis of ameasureable system, such as a power generation plant. Method 100 may beused to generate the one or more comparative analysis models used withinthe maintenance standard 66 described in FIG. 1 . Specifically, method100 determines the usable characteristics and model coefficientsassociated with one or more comparative analysis models that illustratethe correlation between the maintenance quality and future reliability.Method 100 may be implemented using a user and/or computing nodeconfigured to receive inputted data for determining model coefficients.For example, a computing node may automatically receive data and updatemodel coefficients based on received updated data.

Method 100 starts at step 102 and selects one or more target variables(“Target Variables”). The target variable is a quantifiable attributeassociated with the measureable system, such as total operating expense,financial result, capital cost, operating cost, staffing, product yield,emissions, energy consumption, or any other quantifiable attribute ofperformance. Target Variables could be in manufacturing, refining,chemical, including petrochemicals, organic and inorganic chemicals,plastics, agricultural chemicals, and pharmaceuticals, Olefins plant,chemical manufacturing, pipeline, power generating, distribution, andother industrial facilities. Other embodiments of the Target Variablescould also be for different environmental aspects, maintenance ofbuildings and other structures, and other forms and types of industrialand commercial industries.

At step 104, method 100 identifies the first principle characteristics.First principle characteristics are the physical or fundamentalcharacteristics of a measurable system or process that are expected todetermine the Target Variable. In one embodiment, the first principlecharacteristics may be the asset unit first principle data or otherasset-level data 64 described in FIG. 1 . Common brainstorming or teamknowledge management techniques can be used to develop the first list ofpossible characteristics for the Target Variable. In one embodiment, allof the characteristics of an industrial facility that may causevariation in the Target Variable when comparing different measureablesystems, such as industrial facilities, are identified as firstprinciple characteristics.

At step 106, method 100 determines the primary first principlecharacteristics from all of the first principle characterizes identifiedat step 104. As will be understood by those skilled in the art, manydifferent options are available to determine the primary first principlecharacteristics. One such option is shown in FIG. 11 , which will bediscussed in more detail below. Afterwards, method 100 moves to step108, to classify the primary characteristics. Potential classificationsfor the primary characteristics include discrete, continuous, orordinal. Discrete characteristics are those characteristics that can bemeasured using a selection between two or more states, for example abinary determination, such as “yes” or “no.” An example discretecharacteristic could be “Duplicate Equipment.” The determination of“Duplicate Equipment” is “yes, the facility has duplicate equipment” or“no, there is no duplicate equipment.” Continuous characteristics aredirectly measurable. An example of a continuous characteristic could bethe “Feed Capacity,” since it is directly measured as a continuousvariable. Ordinal characteristics are characteristics that are notreadily measurable. Instead, ordinal characteristics can be scored alongan ordinal scale reflecting physical differences that are not directlymeasurable. It is also possible to create ordinal characteristics forvariables that are measurable or binary. An example of an ordinalcharacteristic would be refinery configuration between three typicalmajor industry options. These are presented in ordinal scale by unitcomplexity:

1.0 Atmospheric Distillation 2.0 Catalytic Cracking Unit 3.0 Coking Unit

The above measurable systems are ranked in order based on ordinalvariables and generally do not contain information about anyquantifiable quality of measurement. In the above example, thedifference between the complexity of the 1.0 measureable system oratmospheric distillation and the 2.0 measureable system or catalyticcracking unit, does not necessarily equal the complexity differencebetween the 3.0 measureable system or coking unit and the 2.0measureable system or catalytic cracking unit.

Variables placed in an ordinal scale may be converted to an intervalscale for development of model coefficients. The conversion of ordinalvariables to interval variables may use a scale developed to illustratethe differences between units are on a measurable scale. The process todevelop an interval scale for ordinal characteristic data can rely onthe understanding of a team of experts of the characteristic’sscientific drivers. The team of experts can first determine, based ontheir understanding of the process being measured and scientificprinciple, the type of relationship between different physicalcharacteristics and the Target Variable. The relationship may be linear,logarithmic, a power function, a quadratic function or any othermathematical relationship. Then the experts can optionally estimate acomplexity factor to reflect the relationship between characteristicsand variation in Target Variable. Complexity factors may be theexponential power used to make the relationship linear between theordinal variable to the Target Variable resulting in an intervalvariable scale. Additionally, in circumstances where no data exist, thedetermination of primary characteristics may be based on expertexperience.

At step 110, method 100 may develop a data collection classificationarrangement. The method 100 may quantify the characteristics categorizedas continuous such that data is collected in a consistent manner. Forcharacteristics categorized as binary, a simple yes/no questionnaire maybe used to collect data. A system of definitions may need to bedeveloped to collect data in a consistent manner. For characteristicscategorized as ordinal, a measurement scale can be developed asdescribed above.

To develop a measurement scale for ordinal characteristics, method 100may employ at least four methods to develop a consensus function. In oneembodiment, an expert or team of experts can be used to determine thetype of relationship that exists between the characteristics and thevariation in Target Variable. In another embodiment, the ordinalcharacteristics can be scaled (for example 1, 2, 3 ... n for nconfigurations). By plotting the target value versus the configuration,the configurations are placed in progressive order of influence. Inutilizing the arbitrary scaling method, the determination of the TargetVariable value relationship to the ordinal characteristic is forced intothe optimization analysis, as described in more detail below. In thiscase, the general optimization model described in Equation 1.0 can bemodified to accommodate a potential non-linear relationship. In anotherembodiment, the ordinal measurement can be scaled as discussed above,and then regressed against the data to make a plot of Target Variableversus the ordinal characteristic to be as nearly linear as possible. Ina further embodiment, a combination of the foregoing embodiments can beutilized to make use of the available expert experience, and availabledata quality and data quantity of data.

Once method 100 establishes a relationship, method 100 may develop ameasurement scale at step 110. For instance, a single characteristic maytake the form of five different physical configurations. Thecharacteristics with the physical characteristics resulting in thelowest effect on variation in Target Variable may be given a scalesetting score. This value may be assigned to any non-zero value. In thisexample, the value assigned is 1.0. The characteristics with the secondlargest influence on variation in Target Variable will be a function ofthe scale setting value, as determined by a consensus function. Theconsensus function is arrived at by using the measurement scale forordinal characteristics as described above. This is repeated until ascale for the applicable physical configurations is developed.

At step 112, method 100 uses the classification system developed at step110 to collect data. The data collection process can begin with thedevelopment of data input forms and instructions. In many cases, datacollection training seminars are conducted to assist in data collection.Training seminars may improve the consistency and accuracy of datasubmissions. A consideration in data collection may involve thedefinition of the measureable system’s, such as an industrial facility,analyzed boundaries. Data input instructions may provide definitions ofwhat measureable systems’ costs and staffing are to be included in datacollection. The data collection input forms may provide worksheets formany of the reporting categories to aid in the preparation of data forentry. The data that is collected can originate from several sources,including existing historical data, newly gathered historical data fromexisting facilities and processes, simulation data from model(s), orsynthesized experiential data derived from experts in the field.

At step 114, method 100 may validate the data. Many data checks can beprogrammed at step 114 of method 100 such that method 100 may acceptdata that passes the validation check or the check is over-ridden withappropriate authority. Validation routines may be developed to validatethe data as it is collected. The validation routines can take manyforms, including: (1) range of acceptable data is specified ratio of onedata point to another is specified; (2) where applicable data is crosschecked against all other similar data submitted to determine outlierdata points for further investigation; and (3) data is cross referencedto any previous data submission judgment of experts. After all inputdata validation is satisfied, the data is examined relative to all thedata collected in a broad “cross-study” validation. This “cross-study”validation may highlight further areas requiring examination and mayresult in changes to input data.

At step 116, method 100 may develop constraints for use in solving thecomparative analysis model. These constraints could include constraintson the model coefficient values. These can be minimum or maximum values,or constraints on groupings of values, or any other mathematicalconstraint forms. One method of determining the constraints is shown inFIG. 12 , which is discussed in more detail below. Afterwards, at step118, method 100 solves the comparative analysis model by applyingoptimization methods of choice, such as linear regression, with thecollected data to determine the optimum set of factors relating theTarget Variable to the characteristics. In one embodiment, thegeneralized reduced gradient non-linear optimization method can be used.However, method 100 may utilize many other optimization methods.

At step 120, method 100 may determine the developed characteristics.Developed characteristics are the result of any mathematicalrelationship that exists between one or more first principlecharacteristics and may be used to express the information representedby that mathematical relationship. In addition, if a linear generaloptimization model is utilized, then nonlinear information in thecharacteristics can be captured in developed characteristics.Determination of the developed characteristics form is accomplished bydiscussion with experts, modelling expertise, and by trial andrefinement. At step 122, method 100 applies the optimization model tothe primary first principle characteristics and the developedcharacteristics to determine the model coefficients. In one embodiment,if developed characteristics are utilized, step 116 through step 122 maybe repeated in an iterative fashion until method 100 achieves the levelof model accuracy.

FIG. 11 is a flow chart of an embodiment of a method 200 for determiningprimary first principle characteristics 106 as described in FIG. 10 . Atstep 202, method 200 determines the effect of each characteristic on thevariation in the Target Variable between measureable systems. In oneembodiment, the method may be iteratively repeated, and a comparativeanalysis model can be used to determine the effect of eachcharacteristic. In another embodiment, method 200 may use a correlationmatrix. The effect of each characteristic may be expressed as apercentage of the total variation in the Target Variable in the initialdata set. At step 204, method 200 may rank each characteristic fromhighest to lowest based on its effect on the Target Variable. Persons ofordinary skill in the art are aware that method 200 could use otherranking criteria.

At step 206, the characteristics may be grouped into one or morecategories. In one embodiment, the characteristics are grouped intothree categories. The first category contains characteristics thataffect a Target Variable at a percentage less than a lower threshold(for example, about five percent). The second category may comprise oneor more characteristics with a percentage between the lower percentageand a second threshold (for example, about 5% and about 20%). The thirdcategory may comprise one or more characteristics with a percentage overthe second threshold (for example, about 20%). Other embodiments ofmethod 200 at step 206 may include additional or fewer categories and/ordifferent ranges.

At step 208, method 200 may remove characteristics from a list ofcharacteristics with Target Variable average variations below a specificthreshold. For example, method 200 could remove characteristics thatinclude first category described above in step 206 (e.g.,characteristics with a percentage of less than about five percent).Persons of ordinary skill in the art are aware that other thresholdscould be used, and multiple categories could be removed from the list ofcharacteristics. In one embodiment, if characteristics are removed, theprocess may repeat at step 202 above. In another embodiment, nocharacteristics are removed from the list until determining whetheranother co-variant relationship exists, as described in step 212 below.

At step 210, method 200 determines the relationships between themid-level characteristics. Mid-level characteristics are characteristicsthat have a certain level of effect on the Target Variable, butindividually do not influence the Target Variable in a significantmanner. Using the illustrative categories, those characteristics in thesecond category are mid-level characteristics. Example relationshipsbetween the characteristics are co-variant, dependent, and independent.A co-variant relationship occurs when modifying one characteristiccauses the Target Variable to vary, but only when another characteristicis present. For instance, in the scenario where characteristic “A” isvaried, which causes the Target Variable to vary, but only whencharacteristic “B” is present, then “A” and “B” have a co-variantrelationship. A dependent relationship occurs when a characteristic is aderivative of or directly related to another characteristic. Forinstance, when the characteristic “A” is only present whencharacteristic “B” is present, then A and B have a dependentrelationship. For those characteristics that are not co-variant ordependent, they are categorized as having independent relationships.

At step 212, method 200 may remove dependencies and high correlations inorder to resolves characteristics displaying dependence with each other.There are several potential methods for resolving dependencies. Someexamples include: (i) grouping multiple dependent characteristics into asingle characteristic, (ii) removing all but one of the dependentcharacteristics, and (iii) keeping one of the dependent characteristics,and creating a new characteristic that is the difference between thekept characteristic and the other characteristics. After method 200removes the dependencies, the process may be repeated from step 202. Inone embodiment, if the difference variable is insignificant it can beremoved from the analysis in the repeated step 208.

At step 214, method 200 may analyze the characteristics to determine theextent of the inter-relationships. In one embodiment, if any of theprevious steps resulted in repeating the process, the repetition shouldbe conducted prior to step 214. In some embodiments, the process may berepeated multiple times before continuing to step 214. At 216, thecharacteristics that result in less than a minimum threshold change inthe impact on Target Variable variation caused by another characteristicare dropped from the list of potential characteristics. An illustrativethreshold could be about 10 percent. For instance, if the variation inTarget Variable caused by characteristic “A” is increased whencharacteristic “B” is present, the percent increase in the TargetVariable variation caused by the presence of characteristic “B” must beestimated. If the variation of characteristic “B” is estimated toincrease the variation in the Target Variable by less than about 10% ofthe increase caused by characteristic “A” alone, characteristic “B” canbe eliminated from the list of potential characteristics. Characteristic“A” can also be deemed then to have an insignificant impact on theTarget Variable. The remaining characteristics are deemed to be theprimary characteristics.

FIG. 12 is a flow chart of an embodiment of a method 300 for developingconstraints for use in solving the comparative analysis model asdescribed in step 116 in FIG. 10 . Constraints are developed on themodel coefficients at step 302. In other words, constraints are anylimits placed on model coefficients. For example, a model coefficientmay have a constraint of a maximum of about 20% effect on contributingto a target variable. At step 354, method 300´s objective function, asdescribed below, is optimized to determine an initial set of modelcoefficients. At step 306, method 300 may calculate the percentcontribution of each characteristic to the Target Variable. There areseveral methods of calculating the percent contribution of eachcharacteristic, such as the “Average Method” described in as describedin U.S. Pat. 7,233,910.

With the individual percent contributions developed, method 300 proceedsto step 308, where each percent contribution is compared against expertknowledge. Domain experts may have an intuitive or empirical feel forthe relative impacts of key characteristics to the overall target value.The contribution of each characteristic is judged against this expertknowledge. At step 310, method 300 may make a decision about theacceptability of the individual contributions. If the contribution isfound to be unacceptable the method 300 continues to step 312. If thecontribution is found to be acceptable the method 300 continues to step316.

At step 312, method 300 makes a decision on how to address or handleunacceptable results of the individual contributions. At step 312, theoptions may include adjusting the constraints on the model coefficientsto affect a solution or deciding that the characteristic set chosencannot be helped through constraint adjustment. If the user decides toaccept the constraint adjustment then method 300 proceeds to step 316.If the decision is made to achieve acceptable results through constraintadjustment then method 300 continues to step 314. At step 314, theconstraints are adjusted to increase or decrease the impact ofindividual characteristics in an effort to obtain acceptable resultsfrom the individual contributions. Method 300 continues to step 302 withthe revised constraints. At step 316, peer and expert review of themodel coefficients developed may be performed to determine theacceptability of the model coefficients developed. If the factors passthe expert and peer review, method 300 continues to step 326. If themodel coefficients are found to be unacceptable, method 300 continues tostep 318.

At step 318, method 300 may obtain additional approaches and suggestionsfor modification of the characteristics developed by working withexperts in the particular domain. This may include the creation of newor updated developed characteristics, or the addition of new or updatedfirst principle characteristics to the analysis data set. At step 320, adetermination is made as to whether data exists to support theinvestigation of the approaches and suggestions for modification of thecharacteristics. If the data exists, method 300 proceeds to step 324. Ifthe data does not exist, method 300 proceeds to step 322. At step 322,method 300 collects additional data in an effort to make the correctionsrequired to obtain a satisfactory solution. At step 324, method 300revises the set of characteristics in view of the new approaches andsuggestions. At step 326, method 400 may document the reasoning behindthe selection of characteristics. The documentation can be used inexplaining results for use of the model coefficients.

FIG. 13 is a schematic diagram of an embodiment of a model coefficientmatrix 10 for determining model coefficients as described in FIGS. 10-12. While model coefficient matrix 10 can be expressed in a variety ofconfigurations, in this particular example, the model coefficient matrix10 may be construed with the first principle characteristics 12 andfirst developed characteristics 14 on one axis, and the differentfacilities 16 for which data has been collected on the other axis. Foreach first principle characteristic 12 at each facility 16, there is theactual data value 18. For each first principle characteristic 12 anddeveloped characteristic 14, there is the model coefficient 22 that willbe computed with an optimization model. The constraints 20 limit therange of the model coefficients 22. Constraints can be minimum ormaximum values, or other mathematical functions or algebraicrelationships. Moreover, constraints 20 can be grouped and furtherconstrained. Additional constraints 20 on facility data, andrelationships between data points similar to those used in the datavalidation step, and constraints 20 can employ any mathematicalrelationship on the input data can also be employed. In one embodiment,the constraints 20 to be satisfied during optimization apply only to themodel coefficients.

The Target Variable (actual) column 24 comprises actual values of theTarget Variable as measured for each facility. The Target Variable(predicted) column 26 comprises the values for the target value ascalculated using the determined model coefficients. The error column 28comprises the error values for each facility as determined by theoptimization model. The error sum 30 is the summation of the errorvalues in error column 28. The optimization analysis, which comprisesthe Target Variable equation and an objection function, solves for themodel coefficients to minimize the error sum 30. In the optimizationanalysis, the model coefficients αj are computed to minimize the error∈i over all facilities. The non-linear optimization process determinesthe set of model coefficients that minimizes this equation for a givenset of first principle characteristics, constraints, and a selectedvalue.

The Target Variable may be computed as a function of the characteristicsand the to-be-determined model coefficients. The Target Variableequation is expressed as:

$\text{Target Variable equation:}TV_{i} = {\sum\limits_{j}{\alpha_{j}f\left( \text{characteristic} \right)_{ij} + \varepsilon_{i}}}$

where TVi represents the measured Target Variable for facility i; thecharacteristic variable represents a first principle characteristic; fis either a value of the first principle characteristic or a developedprinciple characteristic; i represents the facility number; j representsthe characteristic number; αj represents the jth model coefficient,which is consistent with the jth principle characteristic; and ∈irepresents the error of the model’s TV prediction as defined by theactual Target Variable value minus the predicted Target Variable valuefor facility i.

The objective function has the general form:

$\text{Objective Function: Min}\left\lbrack {\sum\limits_{i = 1}^{m}\left| \varepsilon_{i} \right|^{p}} \right\rbrack^{1/p}\text{,}p \geq 1$

where i is the facility; m represents the total number of facilities;and p represents a selected value

One common usage of the general form of objective function is tominimize the absolute sum of error by using p=1 as shown below:

$\text{Objective Function: Min}\left\lbrack {\sum\limits_{i = 1}^{m}\left| \varepsilon_{i} \right|} \right\rbrack$

Another common usage of the general form of objective function is usingthe least squares version corresponding to p=2 as shown below:

$\text{Objective Function: Min}\left\lbrack {\sum\limits_{i = 1}^{m}\left| \varepsilon_{i} \right|^{2}} \right\rbrack^{1/2}$

Since the analysis involves a finite number of first principlecharacteristics and the objective function form corresponds to amathematical norm, the analysis results are not dependent on thespecific value of p. The analyst can select a value based on thespecific problem being solved or for additional statistical applicationsof the objective function. For example, p=2 is often used because of itsstatistical application in measuring data and Target Variable variationand Target Variable prediction error.

A third form of the objective function is to solve for the simple sum oferrors squared as given in Equation 5 below.

$\text{Objective Function: Min}\left\lbrack {\sum\limits_{i = 1}^{m}\left| \varepsilon_{i} \right|^{2}} \right\rbrack$

While several forms of the objective function have been shown, otherforms of the objective function for use in specialized purposes couldalso be used. Under the optimization analysis, the determined modelcoefficients are those model coefficients that result in the leastdifference between the summation and the actual value of the TargetVariable after the model iteratively moves through each facility andcharacteristic such that each potential model coefficient, subject tothe constraints, is multiplied against the data value for thecorresponding characteristic and summed for the particular facility.

For illustrative purposes, a more specific example of the one or moreembodiments used to determine model coefficients for use in comparativeperformance analysis as illustrated in FIGS. 10-12 is discussed below. ACat Cracker may be a processing unit in most petroleum refineries. A CatCracker cracks long molecules into shorter molecules within the gasolineboiling range and lighter. The process is typically conducted atrelatively high temperatures in the presence of a catalyst. In theprocess of cracking the feed, coke is produced and deposited on thecatalyst. The coke is burned off the catalyst to recover heat and toreactivate the catalyst. The Cat Cracker has several main sections:Reactor, Regenerator, Main Fractionator, and Emission Control Equipment.Refiners may desire to compare the performance of their Cat Crackers tothe performance of Cat Crackers operated by their competitors. Theexample of comparing different Cat Cracker example and may not representthe actual results of applying this methodology to Cat Crackers, or anyother industrial facility. Moreover, the Cat Cracker example is but oneexample of many potential embodiments used to compare measurablesystems.

Using FIG. 10 as an example, method 100 starts at step 102 anddetermines that the Target Variable will be “Cash Operating Costs” or“Cash OPEX” in a Cat Cracker facility. At step 104, the first principlecharacteristics that may affect Cash Operating Costs for a Cat Crackermay include one or more of the following: (1) feed quality; (2)regenerator design; (3) staff experience; (4) location; (5) age of unit;(6) catalyst type; (7) feed capacity; (8) staff training; (9) tradeunion; (10) reactor temperature; (11) duplicate equipment; (12) reactordesign; (13) emission control equipment; (14) main fractionator design;(15) maintenance practices; (16) regenerator temperature; (17) degree offeed preheat; (18) staffing level.

To determine the primary characteristics, method 100 may at step 106determine the effects of the first characteristics. In one embodiment,method 100 may implement step 106 by determining primary characteristicsas shown in FIG. 11 . In FIG. 11 , at step 202, method 200 may assign avariation percentage for each characteristic. At step 204, method 200may rate and rank the characteristics from the Cat Cracker Example. Thefollowing chart shows the relative influence and ranking for at leastsome of the example characteristics in Table 1:

TABLE 1 Characteristics Category Comment Feed Quality 3 Several aspectsof feed quality are key Catalyst Type 3 Little effect on costs, largeimpact on yields Reactor Design. 1 Several key design factors are keyRegenerator Design 3 Several design factors are key Staffing Levels 2Feed Capacity 1 Probably single-most highest impact Emission ControlEquipment 2 Wet versus dry is a key difference Staff Experience 3 Littleeffect on costs Staff Training 2 Little effect on costs MainFractionator Design 3 Little effect on costs, large impact on yieldsLocation 3 Previous data analysis shows this characteristic has littleeffect on costs Trade Union 3 Previous data analysis shows thischaracteristic has little effect on costs Maintenance Practices 2 Effecton reliability and “lost opportunity cost” Age of Unit 2 Previous dataanalysis shows this characteristic has little effect on costs ReactorTemperature 3 Little effect on costs Regenerator Temperature 3 Littleeffect on costs Duplicate Equipment 3 Little effect on costs

In this embodiment, the categories are as follows as shown in Table 2:

TABLE 2 Percent of Average Variation in the Target Variable BetweenFacilities Category 1 (Major Characteristics) >20% Category 2 (MidlevelCharacteristics) 5-20% Category 3 (Minor Characteristics) <5%

Other embodiments could have any number of categories and that thepercentage values that delineate between the categories may be alteredin any manner.

Based on the above example rankings, method 200 groups thecharacteristics according to category at step 206. At step 208, method200 may discard characteristics in Category 3 as being minor. Method 200may analyze characteristics in Category 2 to determine the type ofrelationship they exhibit with other characteristics at step 210. Method200 may classify each characteristic as exhibiting either co-variance,dependence, or independence at step 212. Table 3 is an example ofclassifying the characteristics of the Cat Cracker facility:

TABLE 3 Classification of Category 2 Characteristics Based on Type ofRelationship Category 2 characteristics Type of Relationship IfCo-variant or Dependent, Related Partner(s) Staffing Levels IndependentEmission Equipment Co-variant Maintenance Practice Maintenance PracticesCo-variant StaffExperience Age of Unit Dependent Staff Training StaffTraining Co-variant Maintenance Practice

At step 214, method 200 may analyze the degree of the relationship ofthese characteristics. Using this embodiment for the Cat Crackerexample: staffing levels, which is classified as having an independentrelationship, may stay in the analysis process. Age of Unit isclassified as having a dependent relationship with Staff Training. Adependent relationship means Age of Unit is a derivative of StaffExperience or vice versa. After further consideration, method 200 maydecide to drop the Age of Unit characteristic from the analysis and thebroader characteristic of Staff Training may remain in the analysis. Thethree characteristics classified as having a co-variant relationship,Staff Training, Emission Equipment, Maintenance Practices, must beexamined to determine the degree of co-variance.

Method 200 may determine that the change in Cash Operating Costs causedby the variation in Staff Training may be modified by more than 30% bythe variation in Maintenance Practices. Along the same lines, the changein Cash Operating Costs caused by the variation in Emission Equipmentmay be modified by more than 30% by the variation in MaintenancePractices causing Maintenance Practices, Staff Training and EmissionEquipment to be retained in the analysis process. Method 200 may alsodetermine that the change in Cash Operating Costs caused by thevariation in Maintenance Practice is not modified by more than theselected threshold of 30% by the variation in Staff Experience causingStaff Experience to be dropped from the analysis.

Continuing with the Cat Cracker example and returning to FIG. 10 ,method 100 categorizes the remaining characteristics as continuous,ordinal or binary type measurement in step 108 as shown in Table 4.

TABLE 4 Classification of Remaining characteristics Based on MeasurementType Remaining characteristics Measurement Type Staffing LevelsContinuous Emission Equipment Binary Maintenance Practices Ordinal StaffTraining Continuous

In this Cat Cracker example, Maintenance Practices may have an “economyof scale” relationship with Cash Operating Costs (which is the TargetVariable). An improvement in Target Variable improves at a decreasingrate as Maintenance Practices Improve. Based on historical data andexperience, a complexity factor is assigned to reflect the economy ofscale. In this particular example, a factor of 0.6 is selected. As anexample of coefficients, the complexity factor is often estimated tofollow a power curve relationship. Using Cash Operating Costs as anexample of a characteristic that typically exhibits an “economy ofscale;” the effect of Maintenance Practices can be described with thefollowing:

$\begin{array}{l}{Target\mspace{6mu} Variable_{facility\mspace{6mu} A} =} \\{\left( \frac{Capacity_{facility\mspace{6mu} A}}{Capacity_{facility\mspace{6mu} B}} \right)^{ComplexityFactor} \ast Target\mspace{6mu} Variable_{facilityB}}\end{array}$

At step 110, method 100 may develop a data collection classificationsystem. In this example, a questionnaire may be developed to measure howmany of ten key Maintenance Practices are in regular use at eachfacility. A system of definitions may be used such that the data iscollected in a consistent manner. The data in terms of number ofMaintenance Practices in regular use is converted to a MaintenancePractices Score using the 0.6 factor and “economy of scale” relationshipas illustrated in Table 5.

TABLE 5 Maintenance Practices Score Number Maintenance Practices InRegular Use Maintenance Practices Score 1 1.00 2 1.52 3 1.93 4 2.30 52.63 6 2.93 7 3.21 8 3.48 9 3.74 10 3.98

For illustrative purposes with respect to the Cat Cracker example, atstep 112, method 100 may collect data and at step 114, method 100 mayvalidate the data as shown in Table 6:

TABLE 6 Cat Cracker Data Unit of Measurement Reactor Design Score StaffTraining Man Weeks Staffing Levels Number People Emission Equipment Yes= 1 No= 0 Feed Capacity Barrels per Day Maintenance Practices Score CashOperating Cost Dollars per Barrel Facility #1 1.50 30 50 1 45 3.74 3.20Facility #2 1.35 25 28 1 40 2.30 3.33 Facility #3 1.10 60 8 0 30 1.932.75 Facility #4 2.10 35 23 1 50 3.74 4.26 Facility #5 1.00 25 5 0 252.63 2.32

Constraint ranges were developed for each characteristic by an expertteam to control the model so that the results are within a reasonablerange of solutions as shown in Table 7.

TABLE 7 Cat Cracker Model Constraint Ranges Reactor Design StaffTraining Staffing Levels Emission Equipment Mainte- nance Practices FeedCapac-ity Mini- mum -3.00 -3.00 -1.0 -1.0 0.0 0.0 Maxi- mum 0.00 1.00 400.0 4.0 4.0

At step 116, method 100 produces the results of the model optimizationruns, which are shown below in Table 8.

TABLE 8 Model Results Characteristics Equivalency Factors Reactor Design-0.9245 Staff Training -0.0021 Staffing Levels -0.0313 EmissionEquipment 0.0000 Maintenance Practices 0.0000 Feed Capacity 0.1382

The model indicates Emission Equipment and Maintenance Practices are notsignificant drivers of variations in Cash Operating Costs betweendifferent Cat Crackers. The model may indicate this by finding aboutzero values for model coefficients for these two characteristics.Reactor Design, Staff Training, and Emission Equipment are found to besignificant drivers. In the case of both Emission Equipment andMaintenance Practices, experts may agree that these characteristics maynot be significant in driving variation in Cash Operating Cost. Theexperts may determine that a dependence effect may not have beenpreviously identified that fully compensates for the impact of EmissionEquipment and Maintenance Practices.

FIG. 14 is a schematic diagram of an embodiment of a model coefficientmatrix 10 with respect to the Cat Cracker for determining modelcoefficients for use in comparative performance analysis as illustratedin FIGS. 10-12 . A sample model configuration for the illustrative CatCracker example is shown in FIG. 14 . The data 18, actual values 24, andthe resulting model coefficients 22 are shown. In this example, theerror sum 30 is relatively minimal, so developed characteristics are notnecessary in this instance. In other examples, an error sum of differingvalues may be determined to be significant resulting in having todetermine developed characteristics.

For additional illustrative purposes, another example for determiningmodel coefficients for use in comparative performance analysis asillustrated in FIGS. 10-12 is discussed below. The embodiment willrelate to pipelines and tank farms terminals. Pipelines and tank farmsare assets used by industry to store and distribute liquid and gaseousfeed stocks and products. The example is illustrative for development ofequivalence factors for: (1) pipelines and pipeline systems; (2) tankfarm terminals; and (3) any combination of pipelines, pipeline systemsand tank farm terminals. The example is for illustrative purposes andmay not represent the actual results of applying this methodology to anyparticular pipeline and tank farm terminal, or any other industrialfacility.

Using FIG. 10 as an example, method 100 t, at step 102, selects thedesired Target Variable to be “Cash Operating Costs” or “Cash OPEX” in apipeline asset. For step 104, the first principle characteristics thatmay affect Cash Operating Costs may include for the pipe relatedcharacteristics: (1) type of fluid transported; (2) average fluiddensity; (3) number of input and output stations; (4) total installedcapacity; (5) total main pump driver kilowatt (KW); (6) length ofpipeline; (7) altitude change in pipeline; (8) total utilized capacity;(9) pipeline replacement value; and (10) pump station replacement value.The first principle characteristics that may affect Cash Operating Costsmay include for the tank related characteristics include: (1) fluidclass; (2) number of tanks; (3) total number of valves in terminal; (4)total nominal tank capacity; (5) annual number of tank turnovers; and(6) tank terminal replacement value.

To determine the primary first principle characteristics, method 100determines the effect of the first characteristics at step 106. In oneembodiment, method 100 may implement step 106 by determining primarycharacteristics as shown in FIG. 11 . In FIG. 11 , at step 202, method100 may for each characteristic assign an impact percentage. Thisanalysis shows that the pipeline replacement value and tank terminalreplacement value may be used widely in the industry and arecharacteristics that are dependent on more fundamental characteristics.Accordingly, in this instance, those values are removed fromconsideration for primary first principle characteristics. At step 204,method 200 may rate and rank the characteristics. Table 9 shows therelative impact and ranking for the example characteristics method 200may assign a variation percentage for each characteristic.

TABLE 9 Characteristics Category Comment Type of Fluid TransportedAnnual Number of Tank Turnovers Tank Terminal Replacement Value 2products and crude Average Fluid Density 3 affects power consumptionNumber of Input and Output Stations 1 more stations means more costTotal Installed Capacity 3 surprisingly minor affect Total Main PumpDriver KW 1 power consumptionsumption Length of pipeline 3 no affectAltitude change in pipeline 3 small affect by related to KW TotalUtilized Capacity 3 no effect Pipeline Replacement Value 3 industrystandard has no effect Pump Station Replacement: Value 3 industrystandard has little effect Fluid Class 3 no effect Number of Tanks 2important tank farm parameter Total Number of Valves in Terminal 3 noeffect Total Nominal Tank Capacity 2 important tank farm parameterAnnual Number of Tank Turnovers 3 no effect Tank Terminal ReplacementValue 3 industry standard has little effect

In this embodiment, the categories are as follows as shown in Table 10:

TABLE 10 Per Cent of Average Variation in the Target Variable BetweenFacilities Category 1 (Major Characteristics) >15% Category 2 (MidlevelCharacteristics) 7-15% Category 3 (Minor Characteristics) <7%

Other embodiments could have any number of categories and that thepercentage values that delineate between the categories may be alteredin any manner.

Based on the above example rankings, method 200 groups thecharacteristics according to category at step 206. At step 208, method200 discards those characteristics in Category 3 as being minor. Method200 may further analyze the characteristics in Category 2 to determinethe type of relationship they exhibit with other characteristics at step210. Method 200 classifies each characteristic as exhibiting eitherco-variance, dependence or independence as show below in Table 11:

TABLE 11 Classification of Category 2 Characteristics Based on Type ofRelationship Category 2 characteristics Type of Relationship IfCo-variant, or Dependent. Related Partner(s) Type of Fluid TransportedIndependent Number of Input and Output Stations Independent Total MainPump Driver KW Independent Number of Tanks Independent Total NominalTank Capacity Independent

At step 212, method 200 may resolve the dependent characteristics. Inthis example, there are no dependent characteristics that method 200needs to resolve. At step 214, method 200 may analyze the degree of theco-variance of the remaining characteristics and determine that nocharacteristics are dropped. Method 200 may deem the remaining variablesas primary characteristics in step 218.

Continuing with the Pipeline and Tank Farm example and returning to FIG.10 , method 100 may categorize the remaining characteristics ascontinuous, ordinal or binary type measurement at step 108 as shown inTable 12.

TABLE 12 Classification of Remaining characteristics Based onMeasurement Type Remaining characteristics Measurement Type Type ofFluid Transported Binary Number of Input and Output Stations ContinuousTotal Main Pump Driver KW Continuous Number of Tanks Continuous TotalNominal Tank Capacity Continuous

At step 110, method 100 may develop a data collection classificationsystem. In this example a questionnaire may be developed to collectinformation from participating facilities on the measurements above. Atstep 112, method 100 may collect the data and at step 114, method 100may validate the data as shown in Tables 13 and 14.

TABLE 13 Pipe Line and Tank Farm Data Characteristic Measurement UnitsType of Fluid 1 = Product 2 = Crude Number of Input and Output StationsCount Total Main Pump Driver KW Number of Tanks Count Total Nominal TankCapacity KMT Facility 1 1 8 74.0 34 1,158 Facility 2 2 16 29.0 0 0Facility 3 1 2 5.8 7 300 Facility 4 1 5 4.9 6 490 Facility 5 1 2 5.4 8320 Facility 6 2 2 2.5 33 191 Facility 7 1 3 8.2 0 0 Facility 8 2 2 8.70 0 Facility 9 1 3 15.0 10 180 Facility 10 1 9 12.0 22 860 Facility 11 14 20.0 5 206 Facility 12 2 9 9.3 0 0 Facility 13 2 12 6.2 0 0

TABLE 14 Pipe Line and Tank Farm Data Characteristic Measurement UnitsType of Fluid 1 = Product 2 = Crude Number of Input and Output StationsCount Total Main Pump Driver KW Number of Tanks Count Total Nominal TankCapacity KMT Facility 14 1 5 41.4 19 430 Facility 15 2 8 8.2 0 0Facility 16 1 8 96.8 31 1,720 Facility 17 1 2 15.0 8 294

In step 116, method 100 may develop constraints on the modelcoefficients by the expert as shown below in Table 15.

TABLE 15 Type of Fluid Number of Input and Output Stations Total MainPump Driver Number of Tanks Total Nominal Tank Capacity Minimum 0 0 0134 0 Maximum 2000 700 500 500 100

At step 116, method 100 produces the results of the model optimizationruns, which are shown below in Table 16.

TABLE 16 Model Results Characteristics Equivalency Factors Type of FluidTransported 1301.1 Number of Input and Output Stations 435.4 Total MainPump Driver KW 170.8 Number of Tanks 134.0 Total Nominal Tank Capacity6.11

In step 118, method 100 may determine that there is no need fordeveloped characteristics in this example. The final model coefficientsmay include model coefficients determined in the comparative analysismodel step above.

FIG. 15 is a schematic diagram of an embodiment of a model coefficientmatrix 10 with respect to the pipeline and tank farm for determiningmodel coefficients for use in comparative performance analysis asillustrated in FIGS. 10-12 . This example shows but one of manypotential applications of this invention to the pipeline and tank farmindustry. The methodology described and illustrated in FIGS. 10-15 couldbe applied to many other different industries and facilities. Forexample, this methodology could be applied to the power generationindustry, such as developing model coefficients for predicting operatingexpense for single cycle and combined cycle generating stations thatgenerate electrical power from any combination of boilers, steam turbinegenerators, combustion turbine generators and heat recovery steamgenerators. In another example, this methodology could be applied todevelop model coefficients for predicting the annual cost for ethylenemanufacturers of compliance with environmental regulations associatedwith continuous emissions monitoring and reporting from ethylenefurnaces. In one embodiment, the model coefficients would apply to bothenvironmental applications and chemical industry applications.

FIG. 9 is a schematic diagram of an embodiment of a computing node forimplementing one or more embodiments described in this disclosure, suchas method 60, 100, 200, and 300 as described in FIGS. 1 and 10-12 ,respectively. The computing node may correspond to or may be part of acomputer and/or any other computing device, such as a handheld computer,a tablet computer, a laptop computer, a portable device, a workstation,a server, a mainframe, a super computer, and/or a database. The hardwarecomprises of a processor 900 that contains adequate system memory 905 toperform the required numerical computations. The processor 900 executesa computer program residing in system memory 905, which may be anon-transitory computer readable medium, to perform the methods 60, 100,200, and 300 as described in FIGS. 1 and 10-12 , respectively. Video andstorage controllers 910 may be used to enable the operation of display915 to display a variety of information, such as the tables and userinterfaces described in FIGS. 2-8 . The computing node includes variousdata storage devices for data input such as floppy disk units 920,internal/external disk drives 925, internal CD/DVDs 930, tape units 935,and other types of electronic storage media 940. The aforementioned datastorage devices are illustrative and exemplary only.

The computing node may also comprise one or more other input interfaces(not shown in FIG. 9 ) that comprise at least one receiving deviceconfigured to receive data via electrical, optical, and/or wirelessconnections using one or more communication protocols. In oneembodiment, the input interface may be a network interface thatcomprises a plurality of input ports configured to receive and/ortransmit data via a network. In particular, the network may transmitoperation and performance data via wired links, wireless link, and/orlogical links. Other examples of the input interface may include but arenot limited to a keyboard, universal serial bus (USB) interfaces and/orgraphical input devices (e.g., onscreen and/or virtual keyboards). Inanother embodiment, the input interfaces may comprise one or moremeasuring devices and/or sensing devices for measuring asset unit firstprinciple data or other asset-level data 64 described in FIG. 1 . Inother words, a measuring device and/or sensing device may be used tomeasure various physical attributes and/or characteristics associatedwith the operation and performance of a measurable system.

These storage media are used to enter data set and outlier removalcriteria into to the computing node, store the outlier removed data set,store calculated factors, and store the system-produced trend lines andtrend line iteration graphs. The calculations can apply statisticalsoftware packages or can be performed from the data entered inspreadsheet formats using Microsoft Excel®, for example. In oneembodiment the calculations are performed using either customizedsoftware programs designed for company-specific system implementationsor by using commercially available software that is compatible withMicrosoft Excel® or other database and spreadsheet programs. Thecomputing node can also interface with proprietary or public externalstorage media 955 to link with other databases to provide data to beused with the future reliability based on current maintenance spendingmethod calculations. An output interface comprises an output device fortransmitting data. The output devices can be a telecommunication device945, a transmission device, and/or any other output device used totransmit the processed future reliability data, such as the calculationdata worksheets, graphs and/or reports, via one or more networks, anintranet or the Internet to other computing nodes, network nodes, acontrol center, printers 950, electronic storage media similar to thosementioned as input devices 920, 925, 930, 935, 940 and/or proprietarystorage databases 960. These output devices used herein are illustrativeand exemplary only.

In one embodiment, system memory 905 interfaces with a computer bus orother connection so as to communicate and/or transmit information storedin system memory 905 to processor 900 during execution of softwareprograms, such as an operating system, application programs, devicedrivers, and software modules that comprise program code, and/orcomputer executable process steps, incorporating functionality describedherein, e.g., methods 60, 100, 200, and 300. Processor 900 first loadscomputer executable process steps from storage, e.g., system memory 905,storage medium /media, removable media drive, and/or othernon-transitory storage devices. Processor 900 can then execute thestored process steps in order to execute the loaded computer executableprocess steps. Stored data, e.g., data stored by a storage device, canbe accessed by processor 900 during the execution of computer executableprocess steps to instruct one or more components within the computingnode.

Programming and/or loading executable instructions onto system memory905 and/or one or more processing units, such as a processor ormicroprocessor, in order to transform a computing node 40 into anon-generic particular machine or apparatus that performs modelling usedto estimate future reliability of a measurable system is well-known inthe art. Implementing instructions, real-time monitoring, and otherfunctions by loading executable software into a microprocessor and/orprocessor can be converted to a hardware implementation by well-knowndesign rules and/or transform a general-purpose processor to a processorprogrammed for a specific application. For example, decisions betweenimplementing a concept in software versus hardware may depend on anumber of design choices that include stability of the design andnumbers of units to be produced and issues involved in translating fromthe software domain to the hardware domain. Often a design may bedeveloped and tested in a software form and subsequently transformed, bywell-known design rules, to an equivalent hardware implementation in anASIC or application specific hardware that hardwires the instructions ofthe software. In the same manner as a machine controlled by a new ASICis a particular machine or apparatus, likewise a computer that has beenprogrammed and/or loaded with executable instructions is viewed as anon-generic particular machine or apparatus.

FIG. 18 is a schematic diagram of another embodiment of a computing node40 for implementing one or more embodiments within this disclosure, suchas methods 60, 100, 200, and 300 as described in FIGS. 1 and 10-12 ,respectively. Computing node 40 can be any form of computing device,including computers, workstations, hand helds, mainframes, embeddedcomputing device, holographic computing device, biological computingdevice, nanotechnology computing device, virtual computing device and ordistributed systems. Computing node 40 includes a microprocessor 42, aninput device 44, a storage device 46, a video controller 48, a systemmemory 50, and a display 54, and a communication device 56 allinterconnected by one or more buses or wires or other communicationspathway 52. The storage device 46 could be a floppy drive, hard drive,CD-ROM, optical drive, bubble memory or any other form of storagedevice. In addition, the storage device 42 may be capable of receiving afloppy disk, CD-ROM, DVD-ROM, memory stick, or any other form ofcomputer-readable medium that may contain computer-executableinstructions or data. Further communication device 56 could be a modem,network card, or any other device to enable the node to communicate withhumans or other nodes.

At least one embodiment is disclosed and variations, combinations,and/or modifications of the embodiment(s) and/or features of theembodiment(s) made by a person having ordinary skill in the art arewithin the scope of the disclosure. Alternative embodiments that resultfrom combining, integrating, and/or omitting features of theembodiment(s) are also within the scope of the disclosure. Wherenumerical ranges or limitations are expressly stated, such expressranges or limitations may be understood to include iterative ranges orlimitations of like magnitude falling within the expressly stated rangesor limitations (e.g., from about 1 to about 10 includes, 2, 3, 4, etc.;greater than 0.10 includes 0.11, 0.12, 0.13, etc.). The use of the term“about” means ±±10% of the subsequent number, unless otherwise stated.

Use of the term “optionally” with respect to any element of a claimmeans that the element is required, or alternatively, the element is notrequired, both alternatives being within the scope of the claim. Use ofbroader terms such as comprises, includes, and having may be understoodto provide support for narrower terms such as consisting of, consistingessentially of, and comprised substantially of. Accordingly, the scopeof protection is not limited by the description set out above but isdefined by the claims that follow, that scope including all equivalentsof the subject matter of the claims. Each and every claim isincorporated as further disclosure into the specification and the claimsare embodiment(s) of the present disclosure.

While several embodiments have been provided in the present disclosure,it may be understood that the disclosed embodiments might be embodied inmany other specific forms without departing from the spirit or scope ofthe present disclosure. The present examples are to be considered asillustrative and not restrictive, and the intention is not to be limitedto the details given herein. For example, the various elements orcomponents may be combined or integrated in another system or certainfeatures may be omitted, or not implemented. Well-known elements arepresented without detailed description in order not to obscure thepresent invention in unnecessary detail. For the most part, detailsunnecessary to obtain a complete understanding of the present inventionhave been omitted inasmuch as such details are within the skills ofpersons of ordinary skill in the relevant art.

In addition, the various embodiments described and illustrated in thevarious embodiments as discrete or separate may be combined orintegrated with other systems, modules, techniques, or methods withoutdeparting from the scope of the present disclosure. Other items shown ordiscussed as coupled or directly coupled or communicating with eachother may be indirectly coupled or communicating through some interface,device, or intermediate component whether electrically, mechanically, orotherwise. Other examples of changes, substitutions, and alterations areascertainable by one skilled in the art and may be made withoutdeparting from the spirit and scope disclosed herein.

Although the systems and methods described herein have been described indetail, it should be understood that various changes, substitutions, andalterations can be made without departing from the spirit and scope ofthe invention as defined by the following claims. Those skilled in theart may be able to study the preferred embodiments and identify otherways to practice the invention that are not exactly as described herein.It is the intent of this disclosure that variations and equivalents ofthe invention are within the scope of the claims while the description,abstract, and drawings are not to be used to limit the scope of theinvention. The invention is specifically intended to be as broad as theclaims below and their equivalents.

In closing, it should be noted that the discussion of any reference isnot an admission that it is prior art to the present invention,especially any reference that may have a publication date after thepriority date of this application. At the same time, each and everyclaim below is hereby incorporated into this detailed description orspecification as additional embodiments of the disclosure.

What is claimed is:
 1. A method comprising the steps of: electronicallyreceiving, by a processor, at least the following: facility operatingdata of the one or more operating conditions for each respectivefacility of a plurality of facilities; a model for one or more operatingconditions, wherein the model comprises one or more coefficients;iteratively performing, by the processor, one or more iterations ofoutlier bias reduction in the facility operating data of the pluralityof facilities based at least in part on the model; wherein theiteratively performing the one or more iterations of outlier biasreduction comprises the steps of: determining a set of model predictedvalues; comparing the set of model predicted values to the facilityoperating data to produce a set of error values; removing bias facilityoperating data of one or more performance outlier facilities from thefacility operating data of the plurality of facilities to form anon-biased facility operating data; constructing, based at least in parton the non-biased facility operating data, an updated model for the oneor more operating conditions, wherein the updated model comprises one ormore updated coefficients; determining, by the processor, based at leastin part on the non-biased facility operating data for the one or moreoperating conditions of the one or more performance non-biasedfacilities, one or more non-biased performance standards for the one ormore operating conditions; and tracking, by processor, based at least inpart on the one or more non-biased performance standards and thefacility operating data, operating performance of each respectivefacility of the plurality of facilities.
 2. The computer-implementedmethod of claim 1, wherein the iteratively performing the one or moreiterations of the outlier bias reduction further comprises the steps of:determining a set of first improvement error values for the facilityoperating data; determining a set of second improvement error values forthe non-biased facility operating data; and comparing the at least oneset of first improvement error values with the at least one set ofsecond improvement error values.
 3. The computer-implemented method ofclaim 2, wherein the determination that the one or more terminationcriteria are not satisfied is based on the comparison of the at leastone set of first improvement error values with the at least one set ofsecond improvement error values.
 4. The computer-implemented method ofclaim 3, wherein the determination that the one or more terminationcriteria are not satisfied is based on determining that the one or moretermination criteria have at least one improvement value that does notexceed the difference of the at least one set of first improvement errorvalues and the at least one set of second improvement error values. 5.The computer-implemented method of claim 2, wherein the firstimprovement error values are standard error values.
 6. Thecomputer-implemented method of claim 2, wherein the first improvementerror values are coefficient of determination values.
 7. Thecomputer-implemented method of claim 1, wherein a particular criteriumis a specified number of iterations.
 8. The computer-implemented methodof claim 1, wherein a particular criterium 1 s a convergence criterium.9. The computer-implemented method of claim 1, wherein the set of errorvalues comprises a set of relative error values and a set of absoluteerror values.
 10. The computer-implemented method of claim 9, whereinthe one or more performance outlier facilities are determined as one ormore facilities that have the relative error values and the absoluteerror values for respective facility operating data exceed the one ormore error threshold criteria.
 11. The computer-implemented method ofclaim 1, wherein the repeating steps (i) through (iv) further comprises:recombining the non-biased facility operating data of one or moreperformance non-biased facilities with the bias facility operating dataof the one or more performance outlier facilities to produce thefacility operating data.
 12. A computer system, comprising: at least oneserver, comprising: at least one processor and a non-transient storagesubsystem; wherein the non-transient storage subsystem stores a computerprogram comprising instructions that, when executed by the at least oneprocessor, cause the at least one processor to at least: electronicallyreceive at least the following: facility operating data of the one ormore operating conditions for each respective facility of a plurality offacilities; a model for one or more operating conditions, and whereinthe model comprises one or more coefficients; iteratively perform one ormore iterations of outlier bias reduction in the facility operating dataof the plurality of facilities based at least in part on the model;wherein the iterative performance of the one or more iterations ofoutlier bias reduction comprises computer operations of: determining aset of model predicted values; comparing the set of model predictedvalues to the facility operating data to produce a set of error values;removing bias facility operating data of one or more performance outlierfacilities from the facility operating data of the plurality offacilities to form a non-biased facility operating data; constructing,based at least in part on the non-biased facility operating a data, anupdated model for the one or more operating conditions, wherein theupdated model comprises one or more updated coefficients; determine,based at least in part on the non-biased facility operating data for theone or more operating conditions of the one or more performancenon-biased facilities, one or more non-biased performance standards forthe one or more operating conditions; and track, based at least in parton the one or more non-biased performance standards and the facilityoperating data, operating performance of each respective facility of theplurality of facilities.
 13. The system of claim 12, wherein theoperations of (i) through (iv) further comprise: recombining thenon-biased facility operating data of one or more performance non-biasedfacilities with the bias facility operating data of the one or moreperformance outlier facilities to produce the facility operating data.14. The system of claim 12, wherein the iterative performance of the oneor more iterations of the outlier bias reduction further comprises theoperations of: determining a set of first improvement error values forthe facility operating data; determining a set of second improvementerror values for the non-biased facility operating data; and comparingthe at least one set of first improvement error values with the at leastone set of second improvement error values.
 15. The system of claim 14,wherein the determination that the one or more termination criteria arenot satisfied is based on the comparison of the at least one set offirst improvement error values with the at least one set of secondimprovement error values.
 16. The system of claim 15, wherein thedetermination that the one or more termination criteria are notsatisfied is based on determining that the one or more terminationcriteria have at least one improvement value that does not exceed thedifference of the at least one set of first improvement error values andthe at least one set of second improvement error values.
 17. The systemof claim 14, wherein the first improvement error values are standarderror values.
 18. The system of claim 14, wherein the first improvementvalues are coefficient of determination values.
 19. The system of claim12, wherein a particular termination criterium is a specified number ofiterations.
 20. The system of claim 12, wherein a particular terminationis a convergence criterium.